Goal:
    A : Type  B : Type
  ============================
   (∀ (l : list A) (l0 : ∀ x : A, In x l → B) (H := CoreTactics.block) 
      (f : A → B) (l1 : list A) (g : ∀ x : A, In x l1 → B),
      g = (λ (x : A) (_ : In x l1), f x)
      → {| pr1 := l; pr2 := l0 |} = {| pr1 := l1; pr2 := g |}
        → map_InP l l0 = map_InP l1 g
          → let H0 := CoreTactics.block in map_InP l1 g = map f l1)


DEBUG:Going to execute:
<coq-equations.plugin::refine_ho@0> $1
DEBUG LTAC Evaluated term: (fun_elim ?P ?f ?f0)

Goals:
    A : Type  B : Type
  ============================
   (∀ f : ∀ x : A, In x [] → B,
      (λ (l : list A) (f0 : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f1 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f1 x0)
           → {| pr1 := l; pr2 := f0 |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f1 l0) []
        f [])

    A : Type  B : Type
  ============================
   (∀ (x : A) (xs : list A) (f : ∀ x0 : A, In x0 (x :: xs) → B),
      (λ (l : list A) (f0 : ∀ x0 : A, In x0 l → B) (x0 : list B),
         ∀ (H := CoreTactics.block) (f1 : A → B) (l0 : list A) 
           (g : ∀ x1 : A, In x1 l0 → B),
           g = (λ (x1 : A) (_ : In x1 l0), f1 x1)
           → {| pr1 := l; pr2 := f0 |} = {| pr1 := l0; pr2 := g |}
             → x0 = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f1 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
      → (λ (l : list A) (f0 : ∀ x0 : A, In x0 l → B) (x0 : list B),
           ∀ (H := CoreTactics.block) (f1 : A → B) 
             (l0 : list A) (g : ∀ x1 : A, In x1 l0 → B),
             g = (λ (x1 : A) (_ : In x1 l0), f1 x1)
             → {| pr1 := l; pr2 := f0 |} = {| pr1 := l0; pr2 := g |}
               → x0 = map_InP l0 g
                 → let H0 := CoreTactics.block in map_InP l0 g = map f1 l0)
          (x :: xs) f
          (f x (map_InP_obligations_obligation_1 x xs)
           :: map_InP xs
                (λ (x0 : A) (inx : In x0 xs),
                   f x0 (map_InP_obligations_obligation_2 x xs x0 inx))))


DEBUG:Going to execute:
intros

Goals:
    A : Type  B : Type  f : ∀ x : A, In x [] → B
  ============================
   ((λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
       ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
         (g : ∀ x0 : A, In x0 l0 → B),
         g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
         → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
           → x = map_InP l0 g
             → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) [] f
      [])

  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   ((λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
       ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
         (g : ∀ x0 : A, In x0 l0 → B),
         g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
         → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
           → x = map_InP l0 g
             → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0)
      (x :: xs) f
      (f x (map_InP_obligations_obligation_1 x xs)
       :: map_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               f x0 (map_InP_obligations_obligation_2 x xs x0 inx))))


DEBUG:Going to execute:
cbv beta

Goals:
    A : Type  B : Type  f : ∀ x : A, In x [] → B
  ============================
   (∀ (H := CoreTactics.block) (f0 : A → B) (l : list A) 
      (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := []; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → [] = map_InP l g
          → let H0 := CoreTactics.block in map_InP l g = map f0 l)

  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (H := CoreTactics.block) (f0 : A → B) (l : list A) 
      (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := x :: xs; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → f x (map_InP_obligations_obligation_1 x xs)
          :: map_InP xs
               (λ (x0 : A) (inx : In x0 xs),
                  f x0 (map_InP_obligations_obligation_2 x xs x0 inx)) =
          map_InP l g → let H0 := CoreTactics.block in map_InP l g = map f0 l)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  B : Type  f : ∀ x : A, In x [] → B
  ============================
   (∀ (H := CoreTactics.block) (f0 : A → B) (l : list A) 
      (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := []; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → [] = map_InP l g
          → let H0 := CoreTactics.block in map_InP l g = map f0 l)

  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (H := CoreTactics.block) (f0 : A → B) (l : list A) 
      (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := x :: xs; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → f x (map_InP_obligations_obligation_1 x xs)
          :: map_InP xs
               (λ (x0 : A) (inx : In x0 xs),
                  f x0 (map_InP_obligations_obligation_2 x xs x0 inx)) =
          map_InP l g → let H0 := CoreTactics.block in map_InP l g = map f0 l)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim